Complete weight enumerators of three classes of linear codes

Abstract

In recent years, a great deal of effort has been devoted to the study of linear codes with few weights, since they have applications in secret sharing, authentication codes, association schemes and some other fields. In this paper, we propose three classes of linear codes by using proper defining sets and investigate their complete weight enumerators. As applications, these linear codes are employed to construct secret sharing schemes with access structures and systematic authentication codes. Moreover, we obtain three classes of asymptotically optimal systematic authentication codes.